And that second interpretation is clearly proven wrong by all the other descriptions of the other alignments. I agree that taken on its own, it's ambiguous and it smack a bit of 2e (worst edition ever, for this point amongst others, although the settings were great) where you could theoretically have two lawful good paladins from opposite religions smiting each other because the other one was evil in their view.
I don't have a problem with pallys casting Smite Evil at each other. I think it's a feature illlustrated that alignment isn't that a straightjacket. Conflicting views of what is evil, even among gods, sounds an interesting world to play in.
But if you add the other definitions of good and evil it's obvious that it's not relative to the society, and it's therefore obviously wrong that only the lawful good one would be the only one to be relative.
The rest isn't helping that much.
LG : "I am doing what is expected by society". A relative definition, as you recognized.
NG : "do the best they can to help others according to their needs." Less clearly relative, but still. They'd do the whole human sacrifice as the need of the many outweigh the need of the few.
CG : "act as their conscience directs..." that's the epitome of relative morality. They are not even refering to social norms but only "their conscience"... It's either totally personal but probably at least influenced by the culture he grew up in and his role models... Someone made an example about a child-caring torturer-by-trade upthread... he could fit the CG definition if he thought "I am torturing guilty people, never innocent ones!"
N : "many humans are neutral, they don't take side". So they'll let the sacrifices happen.
CN: "follow their whims". Same as CG, then, except they "hold their personal freedom above all": they do what they want, that's 100% not objective since only them can know what their current whim is.
LE : "methodically take what they want, within the limits of a code of tradition, loyalty, or order" So relative as well, because tradition and loyalty is certainly in setting... "the priest over there demand your heart, don't resist please..." They'd certainly try to get a payment for it, though, since it's just being greedy.
LN : "individuals act in accordance with law, tradition, or personal codes." Another relative, since it's clearly not our laws...
Paradoxically, the only "clearly objective" descriptions are NG, NE "the alignment of those who do whatever they can get away with, without compassion or qualms." and CE "creatures act with arbitrary violence, spurred by their greed, hatred, or bloodlust."